Question

The third proportion to $(x^2-y^2)$ and (x - y), where x and y are unequal, is:

• A. (x + y)
• B. (x - y)
• C. $\frac{x+y}{x-y}$
• D. $\frac{x-y}{x+y}$

Answer 1

The correct option is D

$\frac{x-y}{x+y}$

Let the third proportion to $(x^2-y^2)$ and (x -y) be z.
Then,$(x^2-y^2):(x-y)::(x-y):z$
$z=\frac{(x-y{)}^2}{x^2-y^2}=\frac{x-y}{x+y}$